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Mastering Multi-Step Variable Equations: Rules and Examples

Learn to solve multi-step variable equations with inverse operations. Understand how to isolate the variable by applying the rules of equation-solving. Examples included for practice.

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Mastering Multi-Step Variable Equations: Rules and Examples

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  1. Objective - To solve multi-step variable equations. Example 1 Example 2 x + 3 = 13 2x = 10 - Undo addition by subtracting 3 from both sides. - Undo multiplication by dividing by 2 on both sides. Multi-step equations require two or more inverse operations to solve. 2x + 3 = 13 Subtract 3 from both sides - 3 -3 2x = 10 Divide by 2 on both sides 2 = 2 x = 5

  2. Rules for Solving Equations 1) Goal: Isolate the variable. 2) Undo operations with their opposite operation. 3) Always do the same thing to both sides of the equation. 4) Easiest to undo add/subtract before multiply/divide.

  3. Solve. 3) 7 - x = 12 1) 5x + 4 = 39 -4 -4 -7 -7 - x = 5 5x = 35 5 5 -1 -1 x = -5 x = 7 2) 4) -6 -6 +4 +4 (3) (3) (-5) (-5) -35 = x x = 18

  4. Solve. 6) -(5 - x) = 9 5) 3(x - 2) = 17 3(x) – 3(2) = 17 (-1)(5 + -x) = 9 3x - 6 = 17 +6 +6 (-1)(5) + (-1)(-x) = 9 3x = 23 -5 + x = 9 3 3 +5 +5 x = 14

  5. 8) 7) 12 - 2(x + 4) = 28 (4) (4) 12 + (-2)(x + 4) = 28 5 - y = 160 12 + (-2x) + (-2)(4) = 28 -5 -5 12 + (-2x) + (-8) = 28 -y = 155 12 + (-8) + (- 2x) = 28 (-1) (-1) -2x + 4 = 28 y = -155 -4 -4 -2x = 24 -2 -2 x = -12

  6. Solve. 11) 9) -9 -9 -10 -10 x =-24 x = -18 10) 12) +4 +4 -5 -5 32 = x x = 18

  7. 3 5 13) 14) 2(X -1) = (10 + 5X) X – (3X -9) = -5 X – 3X + 9 = -5 2X – 2 = 6 + 3X -2X + 9 = -5 + 2 +2 -9 -9 2X = 8 + 3X -2X = -14 - 3X - 3X -2 -2 X = 7 -X = 8 X = -8 -1 -1 15) 1 2 1 2 X – 8 = 14 + X + 8 +8 ½ X = 22 + ½ X - ½ X - ½ X No Solution 0 = 22

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